As more and more governments adopt algorithms to support bureaucratic decision-making processes, it becomes urgent to address issues of responsible use and accountability. We examine a contested public service algorithm used in Danish job placement for assessing an individual's risk of long-term unemployment. The study takes inspiration from cooperative audits and was carried out in dialogue with the Danish unemployment services agency. Our audit investigated the practical implementation of algorithms. We find (1) a divergence between the formal documentation and the model tuning code, (2) that the algorithmic model relies on subjectivity, namely the variable which focus on the individual's self-assessment of how long it will take before they get a job, (3) that the algorithm uses the variable "origin"to determine its predictions, and (4) that the documentation neglects to consider the implications of using variables indicating personal characteristics when predicting employment outcomes. We discuss the benefits and limitations of cooperative audits in a public sector context. We specifically focus on the importance of collaboration across different public actors when investigating the use of algorithms in the algorithmic society.